Noise is often present in acquired diagnostic images, such as those obtained from computed tomography (CT) scanning and other x-ray systems, and can be a significant factor in determining how well real intensity interfaces and fine details are preserved in the image. In addition to influencing diagnostic functions, noise also affects many automated image processing and analysis tasks that are crucial in a number of diagnostic applications.
Methods for improving signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) can be broadly divided into two categories: those based on image acquisition techniques and those based on post-acquisition image processing. Improving image acquisition techniques beyond a certain point can introduce other problems and generally requires increasing the overall acquisition time. This risks delivering a higher X-ray dose to the patient and loss of spatial resolution and may require the expense of scanner equipment upgrade.
Post-acquisition filtering, an off-line image processing approach, is often as effective as improving image acquisition without affecting spatial resolution. If properly designed, post-acquisition filtering requires less time and is usually less expensive than attempts to improve image acquisition. Filtering techniques can be classified into two groupings: (i) enhancement, wherein wanted (structure) information is enhanced, ideally without affecting unwanted (noise) information, and (ii) suppression, wherein unwanted information (noise) is suppressed, ideally without affecting wanted information. Suppressive filtering operations may be further divided into two classes: a) space-invariant filtering, and b) space-variant filtering.
Space-invariant filtering techniques, wherein spatially independent fixed smoothing operations are carried out over the entire image, can be effective in reducing noise, but often blur important structures or features within the image at the same time. This can be especially troublesome because details of particular interest often lie along an edge or a boundary of a structure within the image, which can be blurred by conventional smoothing operations.
Space-variant filtering techniques, meanwhile, are less likely to cause blurring of the image. Various methods using space-variant filtering, wherein the smoothing operation is modified by local image features, have been proposed. Diffusive filtering methods based on Perona and Malik's work (1990) [Perona and Malik, “Scale-space and edge detection using anisotropic diffusion”, IEEE Trans. Pattern Analysis. Machine Intelligence, 1990 vol. 12, pp. 629-639] have been adapted to a number of image filtering applications. Using these methods, image intensity at a pixel is diffused to neighboring pixels in an iterative manner, with the diffusion conductance controlled by a constant intensity gradient for the full image. The approach described by Perona and Malik uses techniques that preserve well-defined edges, but apply conventional diffusion to other areas of the 2-D image. While such an approach exhibits some success with 2-D images, however, there are drawbacks. One shortcoming of this type of solution relates to the lack of image-dependent guidance for selecting a suitable gradient magnitude. More particularly, since morphological or structural information is not used to locally control the extent of diffusion in different regions, fine structures often disappear and boundaries that are initially somewhat fuzzy may be further blurred upon filtering when this technique is used.
Three-dimensional imaging introduces further complexity to the problem of noise suppression. Conventional computed tomography CT scanners direct a fan-shaped X-ray beam through the patient or other subject and toward a one-dimensional detector, reconstructing a succession of single slices to obtain a volume or 3-D image. Cone-beam computed tomography or CBCT scanning makes it possible to improve image capture and processing speeds by directing a cone-beam source toward the subject and obtaining the image on a flat-panel X-ray detector. In cone-beam computed tomography scanning, a 3-D image is reconstructed from numerous individual scan projections, each taken at a different angle, whose image data is aligned and processed in order to generate and present data as a collection of volume pixels or voxels.
CBCT scanning is of interest for its advantages in biomedical, dental, and industrial applications. As flat-panel digital x-ray detectors improve in usability and performance, with reduction in image acquisition speed, CBCT shows promise in providing 3-D imaging capabilities at higher image resolution using lower overall radiation dose and with simplified scanner design. However, image noise remains a problem. Using conventional diffusion techniques to reduce image noise can often blur significant features within the 3-D image, making it disadvantageous to perform more than rudimentary image clean-up for reducing noise content.
The processing of CBCT data for obtaining images requires some type of reconstruction algorithm. Various types of image reconstruction have been proposed, generally classified as either (i) exact, (ii) approximate, or (iii) iterative. Exact cone-beam reconstruction algorithms, based on theoretical work of a number of researchers, require that the following sufficient condition be satisfied: “on every plane that intersects the imaged object there exists at least one cone-beam source”, also called the sufficient condition, to be satisfied. The widely used Grangeat algorithm, familiar to those skilled in CBCT image processing, is limited to circular scanning trajectory and spherical objects. Only recently, with generalization of the Grangeat formula, exact reconstruction is possible in spiral/helical trajectory with longitudinally truncated data.
Despite advances in exact methods (i, above), approximate methods (ii) continue to be more widely used. Chief among these CBCT reconstruction approaches and familiar to those skilled in the CT imaging arts are the Feldkamp (FDK) based algorithms.
Advantages of the FDK method include:
1) FDK based algorithms may produce better spatial and contrast resolution, since they need less regularization than do the exact reconstructions;
2) FDK processing produces improved temporal resolution. Reconstruction can be performed using either full-scan or half-scan data. The shorter scanning time improves the temporal resolution, which is critical for applications such as cardiac imaging, lung imaging, CT-guided medical intervention, and orthopaedics;
3) FDK algorithms are computationally efficient. Implementation of the FDK algorithm is relatively simple, straightforward, and processing can be executed in parallel.
The increasing capabilities of high-performance computers and advanced parallel programming techniques contribute to making iterative CBCT reconstruction algorithms (iii) more attractive. As one advantage, iterative approaches appear to have improved capabilities in handling noisy and truncated data. For instance, iterative deblurring via expectation minimization, combined with algebraic reconstruction technique (ART), has been shown to be effective in suppressing noise and metal artifacts.
Image variation is inherent to the physics of image capture and is at least somewhat a result of practical design tolerances. The discrete nature of the x-ray exposure and its conversion to a detected signal invariably results in quantum noise fluctuations. This type of image noise is usually described as a stochastic noise source, whose amplitude varies as a function of exposure signal level within a projected digital image. The resulting relative noise levels, and signal-to-noise ratio (SNR), are inversely proportional to exposure. A second source of image noise is the flat-panel detector and signal readout circuits. In many cases, image noise that is ascribed to non-ideal image capture is modeled as the addition of a random component whose amplitude is independent of the signal level. In practice, however, several external factors, such electro-magnetic interference, can influence both the magnitude and the spatial correlations of image noise due to the detector.
Noise is an inherent aspect of cone beam projection data, especially for low-dose scans. Image filtering, an image processing approach for improving SNR and contrast-to-noise ratio (CNR), is often as effective in compensating for noise as is optimizing the scanner design (hardware) without affecting the image contrast and the image spatio-temporal resolution. If properly designed, filtering requires less time and can be less expensive than improving the hardware.
Filtering methods for 2-D projection data (or sinograms) have been reported in the literature. However, as compared against 2-D considerations, the 3-D noise problem is significantly more complex and does not readily lend itself to 2-D solutions. Among problems not addressed by 2-D solutions is tangential blurring, for example, an artifact familiar to those skilled in 3-D image reconstruction and attributed to angular filtering approaches.
Thus, it is seen that there is a need for improved noise suppression filtering methods that reduce image noise in images obtained from CBCT systems, without compromising sharpness and detail for significant structures or features in the image.